Place eggs in a single layer in a heavy pot that has a tight fitting lid. Cover the eggs by 1- to 2-inches of cool tap water. Add a splash (a tablespoon or so) of cider vinegar to the pan. Place the pan over high heat and bring the water to a full rolling boil. As soon as it hits the full rolling boil, clamp the lid in place and shut the heat off completely. Let the eggs stand, undisturbed for exactly 15 minutes.

When the 15 minutes have passed, carefully carry the pot to the sink and use the lid to hold the eggs back while pouring off the hot water. Give the pan a couple of sharp shakes back and forth and up and down to break the shells a bit. Let a stream of cold tap water pour over the eggs for about 3 minutes.

Working with one egg at a time, use the back of an eating teaspoon to rap the egg all over and break the shells into tiny pieces. Flip the spoon over, hold the egg under a thin stream of cool water and ease the tip of the spoon between the broken shell and the egg. Use the contour of the spoon to pull the shell away from the egg. The running water should remove any leftover shell fragments. Lay the peeled egg on a clean towel.

Repeat with the remaining eggs.

Slice the eggs in half lengthwise and pop the yolks into a bowl (using a spoon to help if necessary.) Either smash the yolks with a fork or potato masher or force through a potato ricer, like I do. Mix 1/4 cup of mayonnaise and 1 tablespoon of Dijon mustard into the squashed yolks with a fork or whisk until smooth. If you'd like the filling to be creamier, add the mayonnaise 1 tablespoon at a time, whisking after each addition and adjust with the remaining Dijon mustard. Add salt and pepper to taste.

Pipe or scoop the filling into the egg white halves. Serve immediately -topped as desired- or wrap before topping and refrigerate until it is time to serve.